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On Cellular Automaton Approaches to Modeling Biological Cells

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Mathematical Systems Theory in Biology, Communications, Computation, and Finance

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 134))

Abstract

We discuss two different types of Cellular Automata (CA): lattice-gas-based cellular automata (LGCA) and the cellular Potts model (CPM), and describe their applications in biological modeling.

LGCA were originally developed for modeling ideal gases and fluids. We describe several extensions of the classical LGCA model to self-driven biological cells. In particular, we review recent models for rippling in myxobacteria, cell aggregation, swarming, and limb bud formation. These LGCA-based models show the versatility of CA in modeling and their utility in addressing basic biological questions.

The CPM is a more sophisticated CA, which describes individual cells as extended objects of variable shape. We review various extensions to the original Potts model and describe their application to morphogenesis; the development of a complex spatial structure by a collection of cells. We focus on three phenomena: cell sorting in aggregates of embryonic chicken cells, morphological development of the slime mold Dictyostelium discoideum and avascular tumor growth. These models include intercellular and extracellular interactions, as well as cell growth and death.

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Authors and Affiliations

  1. Department of Mathematics and Interdisciplinary Center for the Study of Biocomplexity, University of Notre Dame, 46556-5670, Notre Dame, IN, USA

    Mark S. Alber

  2. Department of Mathematics, University of Notre Dame, 46556-5670, Notre Dame, IN, USA

    Maria A. Kiskowski

  3. Department of Physics and Biocomplexity Institute, Indiana University, 47405-7105, Bloomington, IN, USA

    James A. Glazier

  4. Theoretical Division, Los Alamos National Laboratory, 87545, Los Alamos, NM, USA

    Yi Jiang

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  1. Mark S. Alber
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  4. Yi Jiang
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  1. Department of Mathematics, University of Notre Dame, 46556, Notre Dame, IN, USA

    Joachim Rosenthal

  2. Department of Mathematics and Statistics, Texas Tech University, 79409, Lubbock, TX, USA

    David S. Gilliam

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Alber, M.S., Kiskowski, M.A., Glazier, J.A., Jiang, Y. (2003). On Cellular Automaton Approaches to Modeling Biological Cells. In: Rosenthal, J., Gilliam, D.S. (eds) Mathematical Systems Theory in Biology, Communications, Computation, and Finance. The IMA Volumes in Mathematics and its Applications, vol 134. Springer, New York, NY. https://doi.org/10.1007/978-0-387-21696-6_1

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